Matheuristics:survey and synthesis

In integer programming and combinatorial optimisation, people use the term matheuristics to refer to methods that are heuristic in nature, but draw on concepts from the literature on exact methods. We survey the literature on this topic, with a particular emphasis on matheuristics that yield both primal and dual bounds (i.e., upper and lower bounds in the case of a minimisation problem). We also make some comments about possible future developments

Integrated fleet assignment with cargo routing

Master'sMASTER OF ENGINEERIN

Large-scale analytics and optimization in urban transportation : improving public transit and its integration with vehicle-sharing services

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 143-154).Public transportation is undeniably an effective way to move a large number of people in a city. Its ineffectiveness, such as long travel times, poor coverage, and lack of direct services, however, makes it unappealing to many commuters. In this thesis, we address some of the shortcomings and propose solutions for making public transportation more preferable. The first part of this thesis is focused on improving existing bus services to provide higher levels of service. We propose an optimization model to determine limited-stop service to be operated in parallel with local service to maximize total user welfare. Theoretical properties of the model are established and used to develop an efficient solution approach. We present numerical results obtained using real-world data and demonstrate the benefits of limited-stop services. The second part of this thesis concerns the design of integrated vehicle-sharing and public transportation services. One-way vehicle-sharing services can provide better access to existing public transportation and additional options for trips beyond those provided by public transit. The contributions of this part are twofold. First, we present a framework for evaluating the impacts of integrating one-way vehicles haring service with existing public transportation. Using publicly available data, we construct a graph representing a multi-modal transportation service. Various evaluation metrics based on centrality indices are proposed. Additionally, we introduce the notion of a transfer tree and develop a visualization tool that enables us to easily compare commuting patterns from different origins. The framework is applied to assess the impact of Hubway (a bike-sharing service) on public transportation service in the Boston metropolitan area. Second, we present an optimization model to select a subset of locations at which installing vehicle-sharing stations minimizes overall travel time over the integrated network. Benders decomposition is used to tackle large instances. While a tight formulation generally generates stronger Benders cuts, it requires a large number of variables and constraints, and hence, more computational effort. We propose new algorithms that produce strong Benders cuts quickly by aggregating various variables and constraints. Using data from the Boston metropolitan area, we present computational experiments that confirm the effectiveness of our solution approach.by Virot Chiraphadhanakul.Ph.D

La métaheuristique CAT pour le design de réseaux logistiques déterministes et stochastiques

De nos jours, les entreprises d’ici et d’ailleurs sont confrontées à une concurrence mondiale sans cesse plus féroce. Afin de survivre et de développer des avantages concurrentiels, elles doivent s’approvisionner et vendre leurs produits sur les marchés mondiaux. Elles doivent aussi offrir simultanément à leurs clients des produits d’excellente qualité à prix concurrentiels et assortis d’un service impeccable. Ainsi, les activités d’approvisionnement, de production et de marketing ne peuvent plus être planifiées et gérées indépendamment. Dans ce contexte, les grandes entreprises manufacturières se doivent de réorganiser et reconfigurer sans cesse leur réseau logistique pour faire face aux pressions financières et environnementales ainsi qu’aux exigences de leurs clients. Tout doit être révisé et planifié de façon intégrée : sélection des fournisseurs, choix d’investissements, planification du transport et préparation d’une proposition de valeur incluant souvent produits et services au fournisseur. Au niveau stratégique, ce problème est fréquemment désigné par le vocable « design de réseau logistique ». Une approche intéressante pour résoudre ces problématiques décisionnelles complexes consiste à formuler et résoudre un modèle mathématique en nombres entiers représentant la problématique. Plusieurs modèles ont ainsi été récemment proposés pour traiter différentes catégories de décision en matière de design de réseau logistique. Cependant, ces modèles sont très complexes et difficiles à résoudre, et même les solveurs les plus performants échouent parfois à fournir une solution de qualité. Les travaux développés dans cette thèse proposent plusieurs contributions. Tout d’abord, un modèle de design de réseau logistique incorporant plusieurs innovations proposées récemment dans la littérature a été développé; celui-ci intègre les dimensions du choix des fournisseurs, la localisation, la configuration et l’assignation de mission aux installations (usines, entrepôts, etc.) de l’entreprise, la planification stratégique du transport et la sélection de politiques de marketing et d’offre de valeur au consommateur. Des innovations sont proposées au niveau de la modélisation des inventaires ainsi que de la sélection des options de transport. En deuxième lieu, une méthode de résolution distribuée inspirée du paradigme des systèmes multi-agents a été développée afin de résoudre des problèmes d’optimisation de grande taille incorporant plusieurs catégories de décisions. Cette approche, appelée CAT (pour collaborative agent teams), consiste à diviser le problème en un ensemble de sous-problèmes, et assigner chacun de ces sous-problèmes à un agent qui devra le résoudre. Par la suite, les solutions à chacun de ces sous-problèmes sont combinées par d’autres agents afin d’obtenir une solution de qualité au problème initial. Des mécanismes efficaces sont conçus pour la division du problème, pour la résolution des sous-problèmes et pour l’intégration des solutions. L’approche CAT ainsi développée est utilisée pour résoudre le problème de design de réseaux logistiques en univers certain (déterministe). Finalement, des adaptations sont proposées à CAT permettant de résoudre des problèmes de design de réseaux logistiques en univers incertain (stochastique)

A computer graphics approach to logistics strategy modelling

This thesis describes the development and application of a decision support system for logistics strategy modelling. The decision support system that is developed enables the modelling of logistics systems at a strategic level for any country or area in the world. The model runs on IBM PC or compatible computers under DOS (disk operating system). The decision support system uses colour graphics to represent the different physical functions of a logistics system. The graphics of the system is machine independent. The model displays on the screen the map of the area or country which is being considered for logistic planning. The decision support system is hybrid in term of algorithm. It employs optimisation for allocation. The customers are allocated by building a network path from customer to the source points taking into consideration all the production and throughput constraints on factories, distribution depots and transshipment points. The system uses computer graphic visually interactive heuristics to find the best possible location for distribution depots and transshipment points. In a one depot system it gives the optimum solution but where more than one depot is involved, the optimum solution is not guaranteed. The developed model is a cost-driven model. It represents all the logistics system costs in their proper form. Its solution very much depends on the relationship between all the costs. The locations of depots and transshipment points depend on the relationship between inbound and outbound transportation costs. The model has been validated on real world problems, some of which are described here. The advantages of such a decision support system for the formulation of a problem are discussed. Also discussed is the contribution of such an approach at the validation and solution presentation stages

Multi-period sales districting problem

In the sales districting problem, we are given a set of customers and a set of salesmen in some area. The salesmen have to provide services at the customers' locations to satisfy their requirements. The task is to allocate each customer to one salesman, which partitions the set of customers into subsets, called districts. Each district is expected to have approximately equal workload and travel time for each salesman to promote fairness among them. Also, the districts should be geographically compact since they are more likely to reduce unnecessary travel time, which is desirable for economic reasons. Moreover, each customer can require recurring services with different visiting frequencies such as every week or two weeks during a planning horizon. This problem is called the `Multi-Period Sales Districting Problem (MPSDP)' and can be found typically in regular engineering maintenance and sales promotion. In addition to determining the sales districts, we also want to get valid weekly visiting schedules for the salesmen corresponding to the customers' visiting requirements. The schedules should result in weekly districts with the following desirable characteristics: each weekly district should be balanced in weekly workload and geographically compact. The compactness in the schedules provides benefits when a salesman has to deal with short-term requests from customers or change a visiting plan during the week. Namely, the salesman can postpone a visit to another day if necessary, without increasing the travel time too much compared to the original schedule. This is beneficial when the salesman has to deal with unexpected situations, for example, road maintenance, traffic jams, or short notice of time windows from customers. Although the problem is very practical, it has been studied only recently. Since most of the previous literature on general scheduling problems did not consider compactness, a few recent studies have begun to focus on solving the scheduling part of the problem. The purpose of this research is to develop a more sophisticated exact solution approach as well as an efficient high-quality heuristic to solve the scheduling part. Eventually, with an effective elaborate method to solve the scheduling part, we aim for a robust algorithm to solve the districting and scheduling part of the problem simultaneously. This thesis contains three main parts. The first part introduces the problem and provides a mixed-integer linear programming formulation for only the scheduling part and formulation for the whole problem. The second part presents solution approaches, including an exact method and a heuristic, for only the scheduling part. The last part is dedicated to further development of a successful approach from the second part to solve the districting and scheduling part of the problem simultaneously. For solving the scheduling part, Benders' decomposition is developed as a new exact solution method. The linear relaxation of the problem is strengthened by adding several Benders' cuts derived from fractional solutions at the beginning of the algorithm. Moreover, a good-quality integer solution derived from a location-allocation heuristic is used to generate cuts beforehand, which significantly improves the upper bound of the objective function value. Nondominated optimality cuts are implemented to guarantee the strongest Benders' cuts in each iteration. Also, instead of generating a Benders' cut per iteration, we exploit the decomposable structure of the problem formulation to generate multiple cuts per iteration, resulting in a noticeable improvement in the lower bound of the objective function value. In the classical Benders' decomposition, one of the main factors that slow down the algorithm is that one has to solve the integer programmes from scratch in each iteration. To alleviate this problem, a modern implementation creates only one branch-and-bound tree and adds Benders' cuts derived from a solution in each node in a solution cut pool. This method is called branch-and-Benders' cut. To assess the suitability of the algorithm, we compare its performance on small data instances that contain 30$-$50 customers to the Benders' algorithm in CPLEX and show that our algorithm is highly competitive. Since an exact solution method usually struggles to solve realistic large data instances, a meta-heuristic called tabu search is proposed. A high-quality initial solution to start the algorithm is derived from the location-allocation heuristic. Three different neighbourhoods based on information about week centres or customers' week patterns are created within which we search for the best solution. An infeasible solution is allowed in the search to expand the search space. During the search, the size of a whole neighbourhood can be excessively large, so we limit the search to promising areas of the solution space to save computational time. Also, a surrogate objective value is used to save on computational time in cases when computing the real objective value is too time-consuming. Although the tabu search defines a list of forbidden moves to avoid the cycle of solutions, the algorithm can still struggle to avoid being trapped around a local optimum. Therefore, a diversification scheme is proposed for such cases. The algorithm is also accelerated by combining all neighbourhoods and selecting the appropriate neighbourhood for each iteration by a roulette wheel selection. It shows impressive results in small data instances that contain 30$-$50 customers. The comparison with built-in heuristics in CPLEX confirms the robustness of the tabu search algorithm. Finally, we combine the tabu search algorithm with our developed Benders' decomposition. Numerical results show that the tabu search method improves the upper bound of the Benders' decomposition algorithm. However, the overall performance is not satisfying so the combination of these two techniques still requires more proper development. As the tabu search algorithm performs well on the scheduling part, it is extended to solve the whole problem, i.e., the districting and scheduling part at the same time. Computational results on large data instances, which contain between 100 and 300 customers, demonstrate its capacity to derive a high-quality solution within a reasonable amount of time, i.e., less than 17 minutes. At the same time, the Benders' decomposition algorithm in CPLEX, which is a benchmark in this case, and the built-in heuristics in CPLEX cannot even find any feasible integer solution for most of the instances within an hour. Importantly, there is a conflict between the districting part and the scheduling part so we recommend solving both parts simultaneously for tackling the MPSDP. The multi-period sales districting problem is highly practical and challenging to solve. To the best of our knowledge, we are the first to propose a single integrated solution approach to solve the whole problem. Further studies including adding more realistic planning requirements into consideration and effective solution approaches to solve the problem are still required

Network design decisions in supply chain planning

Structuring global supply chain networks is a complex decision-making process. The typical inputs to such a process consist of a set of customer zones to serve, a set of products to be manufactured and distributed, demand projections for the different customer zones, and information about future conditions, costs (e.g. for production and transportation) and resources (e.g. capacities, available raw materials). Given the above inputs, companies have to decide where to locate new service facilities (e.g. plants, warehouses), how to allocate procurement and production activities to the variousmanufacturing facilities, and how to manage the transportation of products through the supply chain network in order to satisfy customer demands. We propose a mathematical modelling framework capturing many practical aspects of network design problems simultaneously. For problems of reasonable size we report on computational experience with standard mathematical programming software. The discussion is extended with other decisions required by many real-life applications in strategic supply chain planning. In particular, the multi-period nature of some decisions is addressed by a more comprehensivemodel, which is solved by a specially tailored heuristic approach. The numerical results suggest that the solution procedure can identify high quality solutions within reasonable computational time